Not quite. The prevailing view among pro-European Brits, which has been the dominant political force in the UK of the last 40 years or so, was to create a very large trade bloc across a wider Europe, including freedom of movement of labour, but without things like the single currency. This differs from especially the classic French view, which was to create a Franco-German superstate which would be structurally incapable of having a war with itself through almost complete unification of a relatively small group of countries.

The collapse of the Berlin wall certainly played into the British vision for a while, then the Euro initially did well causing the federal contingent to be excited, but the structural weaknesses from the Eurozone members not having gone all in on unification, especially for budgetary policy, have swung it temporarily back to the large but loose collective. The split between the French and German experience of the Euro problem is going to prevent any real progress on this point at all since increasingly those two parties are going to disagree on their visions of the future.